On the Beauville form of the known irreducible symplectic varieties

By A. Rapagnetta. 2006

95 citations recorded by the source corpus.

We study the global geometry of O’Grady’s ten-dimensional irreducible symplectic variety. We determine its second Betti number, its Beauville form and its Fujiki constant.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c5918f6bd8bcd9c8c83136ef6b41a6062676636f

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

A survey of Torelli and monodromy results for holomorphic-symplectic varieties (2011, background): “ple [O’G2]. Then H2(X,Z) is isometric to the orthogonal direct sum of H2(S,Z) ⊕ G2, where Sis a K3 surface, and G2 is the negative deﬁnite root lattice of type G2, with Gram matrix −2 3 3 −6 (see [R]). The isometry group O(G2) is equal to the Weyl group of G2 and its extension to H2(X,Z), via the ”
Monodromy and birational geometry of O'Grady's sixfolds (2019, background): “ETTA divisor of the resolution π: X:= Kev(A) → Kv(A) and the strict transform of the locus on non locally free sheaves. By [38, Prop. 3.3.2], there exists a divisor Esuch that 2[E] = [Σ]. By [32] and [39], the classes [e E] and [Be] have divisibility 2 and square respectively −2 and −4. These are th”
Deformation of the O'Grady moduli spaces (2010, methodology): “The first example is studied by O’Grady in [16], the computation of its second Betti number is started in [16] and completed in [21].”
The Fourier Transform for Certain HyperKähler Fourfolds (2013, methodology): “Although in this paper we will be mostly considering hyperkähler varieties which are deformation equivalent to the Hilbert scheme of length-2 subschemes on a K3 surface, in which case by [6, 44] we have cF = 1 (so that the Fujiki constant is equal to 3) and r = 23, we first formulate a more general ”
Holomorphic symplectic geometry: a problem list (2010, unknown): “The lattices of O’Grady’s two examples are computed in [33]; they are also even.”